Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x-y &= 1 \\ 5x-7y &= 4\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $5x = 7y+4$ Divide both sides by $5$ to isolate $x$ $x = {\dfrac{7}{5}y + \dfrac{4}{5}}$ Substitute this expression for $x$ in the first equation. $-({\dfrac{7}{5}y + \dfrac{4}{5}}) - y = 1$ $-\dfrac{7}{5}y - \dfrac{4}{5} - y = 1$ Simplify by combining terms, then solve for $y$ $-\dfrac{12}{5}y - \dfrac{4}{5} = 1$ $-\dfrac{12}{5}y = \dfrac{9}{5}$ $y = -\dfrac{3}{4}$ Substitute $-\dfrac{3}{4}$ for $y$ in the top equation. $-x+ \dfrac{3}{4} = 1$ $-x+\dfrac{3}{4} = 1$ $-x = \dfrac{1}{4}$ $x = -\dfrac{1}{4}$ The solution is $\enspace x = -\dfrac{1}{4}, \enspace y = -\dfrac{3}{4}$.